The combined area is 0.9545.
Given:
The area under the normal curve to the left of z=-2 plus the area
under the normal curve to the right of z = 2.
Area under the normal curve to the left of z = -2 is:
= 0.0228
Area under the normal curve to the right of z = 2
= 0.9772
Combined area is = 0.9545
Therefore The combined area is 0.9545.
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three less than eight times a number is at least 15
The value of Three less than eight times a number is at least 15 is x≥6
What is meant by mathematical equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or explain the overall situation, this is known as an equation.
Given ,
8x
3 less goes to 8x-3
then there is at least 15 which changes to
8x-3≥15
Then solve for x:
add 3 to the sides--> 3x≥15+3
3x≥18
Divide both of the sides by 3
x≥6
Therefore the value of three less than eight times a number is at least 15 is x≥6
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Households in a city produced a total of 125 000 tonnes of waste in 2017. The total amount of waste is expected to fall by 2% each year. Calculate the total amount of waste these households are expected to produce in 2020.
The total amount of waste these households are expected to produce in 2020 is 117,649 tones.
Define Modelling Exponential Decay
A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.A(1 - r)^tA = Present value , r = rate, t = timeGiven,
Total tonnes of waste in 2017 = 125 000 tonnes
The rate of fall each year is = 2%
Now, find the total amount of waste produce in 2020.
There are 3 years from 2017 to 2020.
So, the amount of waste produce is
= 125000 (1 - 2/100) ^ 3
= 125000 (0.98) ^ 3
= 125000 * 0.941192
= 117,649
Hence, the total amount of waste these households are expected to produce in 2020 is 117,649 tones.
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Which western trail stretched 1,300 miles from illinois to utah territory? the mormon trail the santa fe trail the california trail the oregon trail
The Oregon Trail is a western route that runs 1,000 miles from Illinois to Utah Territory.
In American history, the Oregon Trail, also known as the Oregon-California Trail, was an overland route that connected Independence, Missouri, with Oregon City, which is located close to Portland, Oregon, today, in the Willamette River valley. In the nineteenth century, it was one of two major emigration routes to the American West, the other being the southerly Santa Fe Trail from Independence to Santa Fe (now in New Mexico). A spur of the northerly Oregon route, which was a component of the Oregon Trail, headed to the Great Salt Lake region of what is now northern Utah. Additionally, branches from each main trail provided links to places in California.
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Answer:
I can "Confirm" The answer is not Oregon Trail, I believe the answer is "The Mormon Trail "
Step-by-step explanation:
Or "A"
Have a Joyous Day
Directions: Using the digits 1 - 9 at most one time each, fill in the boxes to make each expression evaluate as a perfect square number. Example: 16 = 4 * 4 also equals 8 * 2.
The missing number in the boxes using the concept of perfect square are;
1) 4
2) 7 and 2
3) 4
4) 3 and 9
5) 3
How to interpret perfect squares?A perfect square is defined as a number that is the square of a whole number. For example, 36 is a perfect square being the square of 6. Other perfect squares that are between 0 and 1000 are 1, 4, 9, 16, 25, 3649, 64, e.t.c
1st box: We see it as;
___ * 2 * 2
Using the concept of perfect squares and the pattern given, we can say that the missing number is 4
2nd box: 14 * __ * ___
Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 7 and 2
3rd box: 2 * 8 * ___
Using the concept of perfect squares and the pattern given, we can say that the missing number is 4
4th box: __ * 3 * _____
Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 3 and 9
5th: 3 * ____
Using the concept of perfect squares and the pattern given, we can say that the missing number is 3
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How should regrouping be used to find the sum?.
Procedure for regrouping to find sum is as follows as mentioned.
Regrouping is accomplished by forming groups of tens during operations such as subtraction and addition. Regrouping is the process of rearranging numbers into groups based on place value to make operations easier.
This is known as regrouping because you are rearranging numbers into place value to complete the process.
Assume we want to add 18 and 12, which equals 30.
1. It is best to visualise your problem as a grid when regrouping with addition.
1 2
+ 1 8
2.In this situation, the first addition would be to add 2 and 8, which equals 10. However, there is no place to write 10 on the bottom row. In this case, regrouping is required. To accomplish this, we take the 0 from the 10 and place it in the bottom row, followed by the 1 above our ten's column. Below is an updated grid:
1
12
+1 8
0
3.We must now add up the tens column. In this case, we have three one-digit numbers to add together. This brings us to the correct solution answer, which is 30.
1
1 2
1 8
3 0
Hence, the regrouping is the simplest way to do addition.
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Which expression can be used to show a roster of twenty-four players divided into four teams?.
A roster of twenty-four players divided into four teams can be represented by the expression 24/4.
Given
24 players total
(4) teams total.
This can be expression as = 24 / 4.
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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?
Answer:
The sale price is 39.99 % off
Step-by-step explanation:
To find the percentage off,
take 49.99 - 30.00 = 19.99
Then divide by 49.99
19.99/49.99
39.9879976
The sale price is 39.99 % off
What is the approximate surface area of the prism? 450 cm2 450 cm3 537 cm2 537 cm3
The approximate surface area of the prism is 537 cm².
A 3-dimensional solid prism's base shape determines how much surface area it has. The total area filled by a prism's faces is known as the prism's surface area. A polyhedron with flat faces is called a prism.
The surface area of the prism formula
So,
[surface area ]=
2×[area of the base]+[perimeter of the base]×height
area of the base=10×8.7/2= 43.5 cm²
the perimeter of the base=10×3= 30 cm
height of the prism=15 cm
[surface area ]=2×[43.5]+[30]×15 = 537 cm²
so the approximate surface area of the prism is 537 cm².
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Evan's parents put tile down on the floor in their home. The tiles are different sizes and shapes. One tile has an angle of 98°. Another tile has an angle of 41°. These two tiles are next to each other so that the 98° angle and the 41° angle share a vertex and a side.
What is the measure of the angle that these two angles form?
Answer:
139 degrees
Step-by-step explanation:
you just add both the angles together since they share a vertex
The cot of 2 kg muhroom and 2. 5 kg of turnip i £8. 55. The cot of 3 kg of muhroom and 4 kg of turnip i £13. 10. Work out the cot of a) 1 kg of turnip. B) 1 kg of muhroom
One kilogram of mushrooms costs $2.90, whereas one kilogram of turnips costs $1.10.
An expression that describes the relationship between two or more numbers and variables is called an equation.
Dependent and independent variables are the two different categories. A dependent variable depends on another variable, whereas an independent variable does not depend on other variables.
Let x stand in for the price per kilogram of mushrooms, and y for the price per kilogram of turnips.
2 kg of mushrooms and 2.5 kg of turnips are priced at £8.55.
2x + 2.5y = 8.55 ________(1)
3 kg of mushrooms and 4 kg of turnips are priced at £13.10.
3x + 4y = 13.10 ________(2)
From both equations:
x = 2.9, y = 1.1
A kg of mushrooms costs $2.90, whereas a kg of turnips costs $1.10.
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GIA IS THINKING OF A NUMBER WHICH CALLS N SHE ADDS 4 TO THE NUMBERAND THEN DOUBLES THE SUM
Answer:
Unknown
Step-by-step explanation:
What is N? Can you show the numberline?
Answer:
the answer is 8 or more then 8
The population
decreasing
of a country town is
at a rate of 4% p.a.
How many years will it take for the town's
population of 15000 to fall below 10000?
Answer:
The rate of decrement is given as: r = 4%. From the table, the initial population is. P (0) = 7900. So, the population in t years is. P (t) = P (0) * (1 - r)^t. This gives. P (t) = 7900 * (1 - 4%)^t. Evaluate the difference.
Population after 2 years = P (1 + 4/100)2 = 62500 X (104/100)2
= 62500 × 26/25 X 26/25 = 100 × 26 ×26 = 67600.
Hence, the population after two years will be 67,600.
Is a vertical and horizontal line proportional or non proportional?
8.6 cherry trees: timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without fi rst cutting the tree down. instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. researchers wanting to understand the relationship between these variables for black cherry trees collected data from 31 such trees in the allegheny national forest, pennsylvania. height is measured in feet, diameter in inches (at 54 inches above ground), and volume in cubic feet. (hand, 1994)
It is difficult to determine the exact volume of a cherry tree without cutting it down, but researchers can use other variables, such as height and diameter, to predict the tree's volume. In a study of black cherry trees
What do we understand by volume?The measurement of how much space an item or substance occupies is called volume. The Allegheny National Forest is occupied by the tree's trunk and branches. Typically, the volume of an object or substance is stated in cubic units, such as cubic feet or cubic metres. The volume variables were looked at in order to comprehend them. Given that it is difficult to quantify without cutting the tree down, the volume of the tree was calculated given its height and diameter. This knowledge may be useful in estimating the potential while looking for them.
Typically, the volume of an object or substance is expressed in cubic units, such as cubic feet or cubic metres. It is determined by multiplying an object's length, breadth, and height.
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(BH 10.27) As in Exercise 36 from Chapter 3, there are n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates, A and B. Each voter chooses randomly whom to vote for, independently and with equal probabilities (a) Use a Normal approximation (with continuity correction) to get an approximation for the probability of a tie, in terms of Φ. (b) Use a first-order Taylor expansion (linear approximation) to the approximation from Part (a) to show that the probability of a tie is approximately 1/Ven, where c is a constant (which you should specify).
We have given a election data of n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates, A and B. Thus,
a) Using Normal approximation, the probability of tie the election is φ (1/√n) - φ(-1/√n) in terms of φ
b) Using Talyor expansion, the probability of a tie is approximately c/√n where c = √2/π.
We have given that,
Total number of voters in an election = n where n is large and even .
Number of candidates who elected the election
= 2 = { A,B}
Each voter choose randomly one of both independently.
a) Using Normal approximation we have calculate to the probability of a tie, in terms of Φ.
n is a large even number
let X be a random variable of number of votes
Tie will occur when X = n/2 , here p = 1/2
X ~ Bin (n,1/2) = N (n/2 , n/4)
P(X = n/2) = P(n/2 - 1/2 < X < n/2+1/2)
= P(-1/2/(sqrt(n/4) < Z< 1/2/(sqrt(n/4))
= P(-1/sqrt(n) <Z< 1/sqrt(n))
= φ (1/√n) - φ(-1/√n)
b) Using the Taylor's Expansion in answer of part(a)
φ (x) = 1/√2π ( x - x³/6 + x⁵/40 - x⁷/336+---)
= φ (1/√n) - φ(-1/√n)
= 1/√2π (1/√n - (-1/√n))
= 1/√2π ( 2/√n)
= √2/π ×1/√n = c/√n
where , c = √2/π
Hence, the required probability is c/√n.
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How will the solution of the system Y 2x two thirds and Y 2x one third change if the inequality sign on both inequalities is reversed to?.
The system of inequalities did not have any solution, but after reversing the sign we will get a solution of the system of inequalities.
The inequalities are : y > 2x + 2/3 and y < 2x + 1/3
There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.
Now when the signs are changed we get:
y < 2x + 2/3 and y > 2x + 1/3
The region below the line y = 2x + 2/3 is the solution of the inequality
y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.
Disclaimer: The complete question is :
How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?
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Answer:
There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
Step-by-step explanation:
Sample answer
sienna has 800 yards of fencing to enclose a rectrangular area. find the dimensions of the rectangle that maximise the enclosed area
Area can be maximized by fencing a square of side 200 yards.
Explanation:
Given perimeter of a rectangle, square has the maximum area (proof given below).
Let x be one of the side and a be te perimeter then the other side would be a/2 - x
and area would be x (a/2 - x). The function will be zero when first derivative of the function is equal to zero and second derivative is negative,
As first derivative is − 2 x + a/2 and this will be zero, when − 2 x + a/2 = 0 or x = a/4. Note that second derivative is − 2. Then two sides will be a/4 each that the it would be square.
Hence if perimeter is 800 yards and it is a square, one side would be 800/4 = 200 yards.
Hence area can be maximized by fencing a square of side 200 yards.
As per the area of rectangle, the dimensions of the rectangle that maximize the enclosed area is 200 yard.
Area of rectangle:
The standard formula to calculate the are of the rectangle is.
A = l x b
l refers the length
b refers the breadth
Given,
Sienna has 800 yards of fencing to enclose a rectangular area.
Area can be maximized by fencing a square of side 200 yards.
Here we need to find the dimensions of the rectangle that maximize the enclosed area.
Let us consider x be one of the side and a be the perimeter then the other side would be written as,
=> a/2 - x
And the and area of the rectangle would be
=> x (a/2 - x).
Then the function will be zero when first derivative of the function is equal to zero and second derivative is negative,
So, as per the first derivative is written as,
=> − 2 x + a/2
And this will be zero, when the equation,
=> − 2 x + a/2 = 0 or x = a/4.
Here we have to note that second derivative is − 2.
And then the two sides will be a/4 each that the it would be square.
Therefore, if perimeter is 800 yards and it is a square, one side would be 800/4 = 200 yards.
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2. for each infinite sequence suggested below, give its generating function in closed form, i.e., not as an infinite sum. (use the most obvious choice of form for the general term of each sequence.)
The general term of each sequence that are given are [tex]a_{n} = n+2 / 2[/tex] ; nEN for the each infinite sequence suggested below, give its generating function in closed form, i.e., not as an infinite sum.
The infinite sequence that are generally number's that doesn't have any ending and are called as the infinite sequence and other that have finite sequence which have final numbers.
Here given infinite sequence are :
[tex]a1 =1 , a2= 0 , a3= 0 , a4 = 1.\\closed form of infinite sequence is an = 1 and 0 otherwise.\\sequence that s given is 3,2,4,1,1,1 and\\ a1 = 3 , a2 2 , a3= 4, a4= 1.\\an = 3, n =1, a2 = 2, a3 = 4, \\no n= 1, n=2, n=3 1 otherwise\\Given sequence is 1,3,6,10 ,15 \\then an = n+2 /2.[/tex]
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What is an example of an inverse graph?.
If we consider the function y=2x+1 then the inverse of the function comes to be y=(x−1)/2.
What is an Inverse Function ?Each element in the range of an original function f is mapped to its corresponding element in the domain by the inverse function f ⁻¹.
Finding inverse of a function
It is typical to consider the x values as the domain and the y values as the range when considering an equation. The domain and range of f are reversed by the inverse function, f ⁻¹, as was previously mentioned. Flip the x and the y, then solve for y to determine the inverse of a written function.
Find the inverse.
y=2x+1
1. Switch the x and y.
x=2y+1
2. Then solve the equation for the y value.
x−1=2y
y=(x−1)/2
The graph of the inverse function is the mirror image to y=x axis
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What does 1 square unit look like?.
1 square unit looks like the area of a square with side measuring 1 unit.
According to the question,
We have the following information:
1 square unit
Now, we know that the square units mean that it is the area of the figure. Now, it can be for any figure whether it is a triangle or square or a circle but the measurements of the sides in such a way that the area found using the formulas of the given figure should be 1 square unit.
For example, if the side of the square is 1 unit then the area of the square is 1 square unit.
Hence, 1 square unit looks like the area of a square with side measuring 1 unit.
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recall that two angles are complementary if the sum of their measures is 90. find the measures of two complementary angles if one angle is more than times the other angle.
The measures of the two complementary angles are 28 and 62 degrees
Complementary angles:
In math, the sum of two angles is equal to 90 degrees, they are called complementary angles.
Given,
Here the two angles are complementary if the sum of their measures is 90.
And we need to find the measures of two complementary angles if one angle is more than 6 times the other angle.
Let us consider A is the measure of the smaller angle and B is the measure of the larger angle.
Here we know that they are complementary
=> A + B = 90
Here we also know that,
=> 2A + 6 = B
Now, we have to replace B in the first equation with the second equation, then we get,
=> A + 2A + 6 = 90
Now, solve for A:
=> 3A + 6 = 90
=> 3A = 84
Therefore, the value of A is 28
Then the value of B is,
=> 2(28) + 6 = 62
Therefore, the two angles that complementary are: 28 and 62 degrees
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Prove that in any group of 6 people there are always at least 3 people who either all know one-another or all are strangers to one-another.
Hint: Use the pigeonhole principle.
I don't see how this applies to the pigeonhole principle because I keep imagining a group of 4 strangers, and then 2 friends. This would be 6 total but against what the proof is asking. Maybe I don't understand the proof in question...
In any group of 6 people there always at least 3 people who either all know one-another or all are strangers to one-another.
The Pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.
The Pigeonhole principle applies because every person is related to every other person in two ways, either they know the person or they do not.
Given that there is a group of 6 people.
Let us say A,B,C,D,E,F.
Suppose that A has at least three friends. If any two of these three are friends with each other, then together with A, they are a group of three mutual friends. If none of these are friends with each other, then they are a group of three mutual strangers to themselves.
On the other hand, A has fewer than three friends among the other five people, then there must be at least three that are strangers to A. If any two of these are strangers, then together with A, they are a group of three strangers. If none of them are strangers to each other, then they are a group of at least three mutual friends.
Hence it is proved that, in any group of 6 people there are always at least 3 people who either all know one-another or all are strangers to one-another.
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A regular hexagonal prism is cut by a plane parallel to its base.
What is the shape of the cross section?
rectangle
regular hexagon
irregular hexagon
trapezoid
please help me
Answer:
regular hexagonStep-by-step explanation:
if a regular hexagonal prism is cut by a plane parallel to its base the shape of the cross section will be a regular hexagona kilogram object suspended from the end of a vertically hanging spring stretches the spring centimeters. at time , the resulting mass-spring system is disturbed from its rest state by the force . the force is expressed in newtons and is positive in the downward direction, and time is measured in seconds. determine the spring constant . newtons / meter formulate the initial value problem for , where is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (give your answer in terms of . differential equation: help (equations) initial conditions: and help (numbers) solve the initial value problem for . help (formulas) plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval . if there is no such maximum, enter none. maximum excursion
The maximum movement from point of equilibrium for the spring mass would be 140 m above the point of equilibrium and 140 m below the point of equilibrium for a total of 280 m.
A) To find the spring constant k, we use Hooke's law which states that
F = kx __(1)
where, F is the force in Newtons applies to extend a string by a distance 'x' in meters.
Hence, in the question, F = 10kg x 9.8 m/sec^2 = 98 Newtons(N)
and x = 9.8 cm = 0.098 m.
Substituting these values in (1)
98 = k(0.098)
=> k = 1000.
Hence, The spring constant is k = 1000
B) We use the spring constant k = 1000 calculated in part(A) above to give us our general equation of motion here which is :
Force = -ky___(2)
where y = y(t) is the displacement of the object from its rest state measured positively in the downward direction when force is applied to it.
From Newton's law,
Force = Mass × Acceleration
where, Mass = 10kg and Acceleration = y"(t) = [tex]\frac{d^2y}{dt^2}[/tex].
Further, from the question
we know that at time t = 0, y(0) = 140cos(8(0)) = 140 ,
y'(0)= -8(140)sin(8(0))= 0.
Using all this information we get the following initial - value problem from(2)
10y" = - 1000y __(3)
y(0) = 140 __(4)
y'(0) = 0 __(5)
In (3) above we seek solutions of the form [tex]y = e^p^t[/tex] where p ∈ R and substitute in (3) to get
[tex]e^p^t (p^2 + 100) = 0[/tex]
=> p = ±10i where i = [tex]\sqrt{-1}[/tex]
y(t) = Acos(10t) + Bsin(10t) (6)
where A, B are constants to be determined by initial conditions (4) and (5).
Using (4) in (6) leads to
140 = Acos (10(0)) +Bsin(10(0))
=> 140 = A
So, this get us to
y(t) = 140 cos(10t) + B sin(10t) (7)
Now using (5) in (7)
0 = -1400 sin(10(0)) + 10 Bsin (10(0))
=> 0 = 10B
=> B = 0
Hence, Our solution is y = 140cos(10t)
The maximum movement from point of equilibrium for the spring mass would be 140 m above the point of equilibrium and 140 m below the point of equilibrium for a total of 280 m.
This is the incomplete question:
Complete question is:
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0 , the resulting mass-spring system is disturbed from its rest state by the force. F(t) = 140cos(8t). The force F(t) is expressed in newtons and is positive in the downward direction, and time is measured in seconds.
Determine the spring constant k.
Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y , y', y" , t)
Solve the initial value problem for y(t).
Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval . if there is no such maximum, enter none. maximum excursion.
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10. While on a visit to DC, you measure that the Washington monument casts a shadow 300 feet long. At the same time, your friend who is 6 feet tall is casting a shadow of 3.25 feet. What is the height of the Washington Monument (rounded to the nearest foot)?
The height of the Washington Monument is 553.84 feet.
What is proportion?A proportion is a comparison of two numbers that each represent the parts of a whole.
Given that, while on a visit to DC, you measure that the Washington monument casts a shadow 300 feet long. At the same time, your friend who is 6 feet tall is casting a shadow of 3.25 feet.
Let the height of the Washington Monument be x,
Using proportion,
6/3.25 = x/300
x = 553.84 feet
Hence, The height of the Washington Monument is 553.84 feet.
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In hypothesis testing, the critical value is O a. the probability of a Type II error b. the same as the p-value O c. the probability of a Type I error O d. a number that establishes the boundary of the rejection region
In hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region
The hypothesis testing is defined as the process of collecting the data and using that as inference draw the calculation about the population parameter.
The reject region of the hypothesis testing is defined as the set of values for the test statistic for which the null hypothesis is rejected.
Therefore, the critical value is a number that establishes the boundary of the rejection region of the graph
Hence, in hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region
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What are the different types of cubicles?.
5 types of cubical are: dedicated, Private office, L-shaped, circular, High walled cubicles
Dedicated Cubicles: A professional cubicle is typically mid-sized and can combine various cubicle designs to improve output across a wide range of vocations.Cubicles for private offices: For some people, private office cubicles are the best option. These types of cubicles are typically designed for executive cubicles rather than the plainer designs used for the majority of workers employing drywall and flat materials."L" shaped: These sectional or "L" shaped cubicles can greatly influence the number of diverse looks your cubicle collection can take on. Of course, this view is superior to cubicle stations with three or four sides everywhere.Circular Cubicles: A circular cubicle is another novel feature of the workplace. These can introduce a fresher perspective that is fashionable, a sight that is not typically present in the majority of offices today.High-Walled Cubicles: The majority of workstations kinds can be categorized according to the heights of their panels and walls, which directly affects the amount of employee privacy your business will provide.
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driving at 45 mi/hr, angie leaves the town of gunnison. beth leaves one hour later driving the same route at 55 mi/hr. after some time passes, she catches up with angie. using t to represent beth's driving time, what numbers and/or variables should go in box c?
Number of hours that Beth will take to catch up the Angie is 4.5 hours
The speed of Angie = 45 miles per hour
We know,
Speed = Distance / Time
Distance = Speed × Time
Substitute the values in the equation
In one hour the distance she traveled = 45 × 1
Multiply the numbers
= 45 miles
Beth leaves one hour later driving the same route
The speed of Beth = 55 miles per hour
The relative speed = 55 - 45
= 10 miles per hour
Then the time taken to catch up = 45/10
Divide the numbers
= 4.5 hours
Hence, the Beth will take 4.5 hours to catchup Angie
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the subgraph-isomorphism problem takes two undirected graphs gl and g2, and asks whether g is isomorphic to a subgraph of g2. show that the subgraph-isomorphism problem is np-complete.
The Subgraph Isomorphism Problem is NP and NP-Hard. Therefore, the subgraph isomorphism problem is NP-Complete.
What is Subgraph Isomorphism?
In theoretical computer science, the subgraph isomorphism drawback could be a procedure task during which 2 graphs G and H ar given as input, and one should confirm whether or not G contains a subgraph that's similarity to H.
Proof:
Certificate: Let G be a subgraph of G2. We also know the mapping between the vertices of G1 and G.
Verification: We have to visualize if G1 is isomorphous to G or not. (i) Checking if the mapping could be a bijection and (ii) confirming if, for each edge (u, v) in G1, there's a foothold (f(u), f(v)) gift in G takes polynomial time.
Therefore, the Subgraph similarity downside has polynomial time verifiability and belongs to the NP category.
The Subgraph similarity drawback belongs to NP-Hard –A drawback L belongs to NP-Hard if each NP drawback is reducible to L in polynomial time. To prove that the Subgraph similarity drawback (S) is NP-Hard, we have a tendency to associate degreed} scale back an already celebrated NP-Hard drawback to S for a selected instance. If this reduction is feasible in polynomial time, then S is additionally associate degree NP-Hard drawback. Thus, allow us to scale back the ingroup call drawback (C) that is NP-Complete (hence, all the issues in NP will be reduced to C in polynomial time) to the Subgraph similarity drawback. If this reduction is feasible in polynomial time, each NP drawback will be reduced to S in polynomial time, thereby proving S to be NP-Hard.
Proof:
Let us prove that the Clique Decision Problem reduces to the Subgraph Isomorphism Problem in polynomial time.
Let the input to the set call drawback be (G, k). The output is true if the graph G contains a set of size k (a set of size k may be a subgraph of G). Let G1 be a whole graph of k vertices and G2 be G, where G1, G2 ar inputs to the Subgraph isomorphy drawback. we have a tendency to observe that k n, then a set of size k can't be a subgraph of G. The time taken to form G1 is O(k2) = O(n2) [since k]as the range of edges in a very complete graph of size k = kC2 = k*(k-1)/2. G contains a pack of size k, if and as long as G1 could be a subgraph of G2 (since G1 itself could be a subgraph of G2 and each graph is similarity to itself, the results of the Subgraph similarity downside is true. Thus, G1 is similarity to a subgraph of G2). Hence, if the pack call downside is true, the Subgraph similarity downside is true and the other way around. Therefore, the pack call downside will be reduced to the Subgraph similarity downside in polynomial time for a specific instance.
Thus, the Subgraph Isomorphism Problem is an NP-Hard Problem
hence,
The Subgraph Isomorphism Problem is NP and NP-Hard. Therefore, the subgraph isomorphism problem is NP-Complete.
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What is the practical importance of research?.
The research is important for the students because it helps them to have a detailed analysis of everything. When you have a proper in-depth analysis of any topic, the result comes out to be fruitful and also the knowledge is enhanced.
The research is important for the students because it helps them to have a detailed analysis of everything. When you have a proper in-depth analysis of any topic, the result comes out to be fruitful and also the knowledge is enhanced.
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